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C2×(C22⋊D19)⋊C3 #11744918

order912
isoclinismisoclinic class of (C19⋊C3)⋊Q8
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC2×(C22⋊D19)⋊C3
unambiguous semidirect product(C2×C22⋊D19)⋊C3

Splittings

FittingC23×C19 ⋊ C2×C3
HallC2×C22⋊D19 ⋊ C3
HallC19⋊C3 ⋊ C2×D4
SylowC19 ⋊ C2×C3×D4

Subgroups

subgroupG/H
centerC22C2×D19⋊C3
commutator, cosocleC2×C19C23×C3
FrattiniC2C22×D19⋊C3
FittingC23×C19C2×C3
socleC22×C19C22×C3
hypercenterC23D19⋊C3
hypocenterC19C2×C3×D4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 152

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10597263⋊C3, #10597331⋊C3, ((C22⋊D19)⋊C3)⋊C4, …
maximal normal subgroup of#10597263⋊C3, #10597331⋊C3, ((C22⋊D19)⋊C3)⋊C4, …
maximal quotient ofC2×((C19⋊C3)⋊C4)⋊C4, #10597370⋊C3, C2×(C2×D19⋊C3)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 129);